I have no way of knowing for sure, but I would have thought RG LeTourneau would have made something for the logging industry maybe a bit earlier than that. His Turn-Pulls were designed in the 30's or 40's and I would not be surprised if modifying it to pull wood occurred around then too.
My personal feeling is, there is really no way to tell. Benjamin Holt gets credit for inventing the first "Bulldozer", but RG LeTourneau takes credit for it as well in his book, but the Lombado boys in Waterville Maine had a steam powered Lombard Log Hauler in the woods in 1901. All used tracks and none had bulldozer blades. Benjamin Holt (who started Caterpillar company) traveled to Maine and saw a working version of the Lombard Log Hauler and its track system. The point I am getting at here is that it all depends on what you want to define as "the first machine."
For what it is worth Enchanted Forester...I had no idea forwarders were that old either. As a lover of old woodworking tools, old tractors and logging equipment, I am glad you take care of your machine. Please post a picture of it sometime.